Subgroups — #18009508

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10596927	C₂	1	2	yes	maximal
2	C₈×#64436	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596927	C₄	1	4	yes	—
4	C₄×#64436	C₄	1	1	yes	characteristic
5	C₄×#64436	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₇	C₈	1	2	yes	—
8	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂×#64436	C₈	1	2	yes	—
10	C₂×#64436	C₂×C₄	1	2	yes	—
11	#10596927	C₈	1	8	yes	complemented
12	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₃₇	—	2	2	no	—
16	#64436	—	2	2	no	—
17	#64436	C₂×C₈	1	4	yes	—
18	C₂²×C₃₇	C₄×C₈	1	1	yes	characteristic
19	C₄×C₃₇	C₄×C₈	1	2	yes	—
20	C₄×C₃₇	M₃₂	1	2	yes	—
21	C₄×C₃₇	M₃₂	1	2	yes	—
22	#1311	—	37	1	no	maximal, Sylow
23	C₂×C₃₇	C₈²	1	1	yes	characteristic
24	C₂×C₃₇	#346	1	1	yes	characteristic
25	C₂×C₃₇	#346	1	1	yes	characteristic
26	C₄×C₁₆	—	37	2	no	—
27	C₈²	—	37	1	no	—
28	C₃₇	#1311	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	—	37	4	no	—
30	C₄×C₈	—	37	1	no	—
31	C₄×C₈	—	37	1	no	—
32	C₄×C₈	#3866	1	1	yes	characteristic
33	C₂×C₈	—	37	2	no	—
34	C₂×C₈	—	37	2	no	—
35	C₂×C₈	#64438	1	2	yes	—
36	C₄²	C₂×#3866	1	1	yes	characteristic
37	C₁₆	—	37	8	no	—
38	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₄×#3866	1	1	yes	characteristic
40	C₂×C₄	C₂×#64438	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	—	37	4	no	—
43	C₈	—	74	2	no	—
44	C₂²	C₄×#64438	1	1	yes	characteristic
45	C₄	C₈×#3866	1	2	yes	—
46	C₄	#11924610	1	2	yes	—
47	C₄	#11924611	1	2	yes	—
48	C₂	C₈×#64438	1	1	yes	characteristic
49	C₂	#14558421	1	1	yes	characteristic
50	C₂	#14558422	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#3866
commutator	C₂×C₃₇	C₈²
Fitting	C₄×C₈×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	C₄×C₈
cosocle	C₄×#64436	C₂²
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	#1311
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
11. #10596927	C₈	semidirect
28. C₃₇	#1311	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#10596927	2
C₈×#64436	2
#1311	37